[en] For a class of square continuous time nonlinear controllers we design a suitable resetting rule inspired by the resetting rule for Clegg integrators and First Order Reset Elements (FORE). With this rule, we prove that the arising hybrid system with temporal regularization is passive in the conventional continuous time sense with a small shortage of input passivity decreasing with the temporal regularization constant. Based on the passivity property, we then investigate the finite gain stability of the interconnection between this passive controller and a passive nonlinear plant.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Forni, Fulvio ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation
Nešić, Dragan; University of Melbourne, Australia > EEE Department
Beker, O., C.V. Hollot and Y. Chait (2001). Plant with an integrator: an example of reset control overcoming limitations of linear feedback. IEEE Transactions Automatic Control 46, 1797-1799. (Pubitemid 33120667)
Beker, O., C.V. Hollot, Y. Chait and H. Han (2004). Fundamental properties of reset control systems. Automatica 40, 905-915.
Cai, C. and A.R. Teel (2009). Characterizations of inputto-state stability for hybrid systems. Systems & Control Letters 58(1), 47-53.
Carrasco, J., A. Banos and A. Van der Schaft (2010). A passivity-based approach to reset control systems stability. Systems & Control Letters 59(1), 18-24.
Clegg, J.C. (1958). A nonlinear integrator for servomechanisms. Trans. A. I. E. E. 77 (Part II), 41-42.
Collins, P. (2004). A trajectory-space approach to hybrid systems. In: International Symposium on the Mathematical Theory of Networks and Systems. Leuven, Belgium.
Fantoni, I., R. Lozano and M.W. Spong (2000). Energy based control of the pendubot. Automatic Control, IEEE Transactions on 45(4), 725-729.
Goebel, R. and A.R. Teel (2006). Solutions to hybrid inclusions via set and graphical convergence with stability theory applications. Automatica 42(4), 573 - 587. (Pubitemid 43267651)
Goebel, R., R. Sanfelice and A.R. Teel (2009). Hybrid dynamical systems. Control Systems Magazine, IEEE 29(2), 28-93.
Horowitz, I. and P. Rosenbaum (1975). Non-linear design for cost of feedback reduction in systems with large parameter uncertainty. Int. J. Contr 21, 977-1001.
Johansson, K.H., J. Lygeros, S. Sastry and M. Egerstedt (1999). Simulation of Zeno hybrid automata. In: Conference on Decision and Control. Phoenix, Arizona. pp. 3538-3543. (Pubitemid 30575121)
Khalil, H.K. (2002). Nonlinear Systems. 3rd ed. Prentice Hall. USA.
Morabito, F., S. Nicosia, A.R. Teel and L. Zaccarian (2004). Measuring and improving performance in anti-windup laws for robot manipulators. In: Advances in Control of Articulated and Mobile Robots (B. Siciliano, A. De Luca, C. Melchiorri and G. Casalino, Eds.). Chap. 3, pp. 61-85. Springer Tracts in Advanced Robotics.
Nešić, D., L. Zaccarian and A.R. Teel (2008). Stability properties of reset systems. Automatica (B) 44(8), 2019-2026.
van der Schaft, A. (1999). L2-Gain and Passivity in Nonlinear Control. second ed. Springer-Verlag New York, Inc. Secaucus, N.J., USA.
Zaccarian, L., D. Nešić and A.R. Teel (2005). First order reset elements and the Clegg integrator revisited. In: American Control Conference. Portland (OR), USA. pp. 563-568. (Pubitemid 41189436)
